Transcript cos
Slide 1
Trigonometry
Measures of triangle
Remember
Angles of triangle add to 180˚
Right-angled triangle
opposite
adjacent
M May
Slide 2
C
b
opposite
A
Cah
cos x =
hypotenuse
a
x
B
c
adjacent
cos x =
12
Cah
13
C
13
5
x
A
12
B
x = cos-1( 12/13)
x = 22.6
M May
Slide 3
cos 60˚ = 0.5
cos 30˚ = 0.866
cos x˚ = 0.5
x˚ = cos-1 (0.5)
x˚ = 60˚
cos x ˚ = 0.8
x˚ = cos-1 (0.8)
x˚ = 36.9˚
cos 45˚ = 0.707
cos 15˚ = 0.966
cos 0˚ =
1
cos 90˚ = 0
cos 10˚ =
0.985
cos 20˚ =
0.940
cos 35˚ =
0.819
cos 80˚ = 0.174
cos 40˚ =
0.766
cos x˚ = 0.65
x˚ = cos-1 (0.65)
x˚ = 49.5˚
cos x˚ = 0.33
x˚ = cos -1 (0.33)
x˚ = 71˚
cos x˚ = 0.12
x˚ = cos -1 (0.12)
x˚ = 83˚
cos x˚ = 0.47
x˚ = cos -1 (0.47)
x˚ = 62˚
cos x˚ = 0.83
x˚ = cos -1 (0.83)
x˚ = 34˚
cos x˚ = 0.05
x˚ = cos -1 (0.05)
x˚ = 87˚
cos x˚ = 0.21
x˚ = cos -1 (0.21)
x˚ = 78˚
cos x˚ = 0.72
x˚ = cos -1 (0.72)
x˚ = 44˚
M May
Slide 4
The angle a ramp makes with the horizontal must be 23 ± 3
degrees to be approved by the Council. If this ramp is 4m long
and is placed 2.7 metres from the step, will it be approved?
3m
x
2.7 m
Soh Cah
√ √ √
cos x = 2.7
3
x = cos-1( 2.7 )
3
x = 25.84193276
x = 25.8˚
So since the angle lies between 20˚ and 26˚ the Council would
approve the ramp.
20˚ < 25.8˚ < 26˚
M May
Slide 5
Use your calculator : cos x˚ = 0.493
x ˚ = cos-1 (0. 493)
cos 30˚ =
cos 69˚ =
cos 47˚ =
cos 23˚ =
cos 54˚ =
cos 62˚ =
cos 73˚ =
cos 78˚ =
cos 90˚ =
cos 4˚ =
x˚=
cos x˚ = 0.639
x ˚ = cos -1 (
x˚=
cos x˚ = 0.866
x˚=
x˚=
)
cos x˚ = 0.234
x˚=
x˚=
cos x˚ = 0.248
x ˚ = cos -1 (
x˚=
cos x˚ = 0.618
x˚=
x˚=
cos x˚ = 0.478
x˚=
x˚=
cos x˚ = 0.476
x˚=
x˚=
M May
Slide 6
Use your calculator : cos x˚ = 0.493
x ˚ = cos-1 (0. 493)
cos 30˚ = 0.866
cos 69˚ = 0.358
cos 47˚ = 0.682
cos 23˚ = 0.921
cos 54˚ = 0.588
cos 62˚ = 0.469
cos 73˚ = 0.292
cos 78˚ = 0.208
cos 90˚ = 0
cos 4˚ = 0.998
x ˚ = 60.5˚
cos x˚ = 0.866
x ˚ = cos-1(0.866)
x ˚ = 30˚
cos x˚ = 0.639
x ˚ = cos -1 ( 0.639 )
x ˚ = 50.3˚
cos x˚ = 0.234
x ˚ = cos-1(0.234)
x ˚ = 76.5˚
cos x˚ = 0.248
x ˚ = cos -1 ( 0.248)
x ˚ = 75.6˚
cos x˚ = 0.618
x ˚ = cos-1(0.618)
x ˚ = 51.8˚
cos x˚ = 0.478
x ˚ = cos-1(0.478)
x ˚ = 61.4˚
cos x˚ = 0.476
x ˚ = cos-1(0.476)
x ˚ = 61.6˚
M May
Slide 7
Soh Cah Toa
Remember
The cosine of an angle is found using
hypotenuse
Cah
cos x =
x
Adjacent
9
cos x =
15
x
12
12
15
x = cos-1(12/15)
x = 36.9˚
M May
Trigonometry
Measures of triangle
Remember
Angles of triangle add to 180˚
Right-angled triangle
opposite
adjacent
M May
Slide 2
C
b
opposite
A
Cah
cos x =
hypotenuse
a
x
B
c
adjacent
cos x =
12
Cah
13
C
13
5
x
A
12
B
x = cos-1( 12/13)
x = 22.6
M May
Slide 3
cos 60˚ = 0.5
cos 30˚ = 0.866
cos x˚ = 0.5
x˚ = cos-1 (0.5)
x˚ = 60˚
cos x ˚ = 0.8
x˚ = cos-1 (0.8)
x˚ = 36.9˚
cos 45˚ = 0.707
cos 15˚ = 0.966
cos 0˚ =
1
cos 90˚ = 0
cos 10˚ =
0.985
cos 20˚ =
0.940
cos 35˚ =
0.819
cos 80˚ = 0.174
cos 40˚ =
0.766
cos x˚ = 0.65
x˚ = cos-1 (0.65)
x˚ = 49.5˚
cos x˚ = 0.33
x˚ = cos -1 (0.33)
x˚ = 71˚
cos x˚ = 0.12
x˚ = cos -1 (0.12)
x˚ = 83˚
cos x˚ = 0.47
x˚ = cos -1 (0.47)
x˚ = 62˚
cos x˚ = 0.83
x˚ = cos -1 (0.83)
x˚ = 34˚
cos x˚ = 0.05
x˚ = cos -1 (0.05)
x˚ = 87˚
cos x˚ = 0.21
x˚ = cos -1 (0.21)
x˚ = 78˚
cos x˚ = 0.72
x˚ = cos -1 (0.72)
x˚ = 44˚
M May
Slide 4
The angle a ramp makes with the horizontal must be 23 ± 3
degrees to be approved by the Council. If this ramp is 4m long
and is placed 2.7 metres from the step, will it be approved?
3m
x
2.7 m
Soh Cah
√ √ √
cos x = 2.7
3
x = cos-1( 2.7 )
3
x = 25.84193276
x = 25.8˚
So since the angle lies between 20˚ and 26˚ the Council would
approve the ramp.
20˚ < 25.8˚ < 26˚
M May
Slide 5
Use your calculator : cos x˚ = 0.493
x ˚ = cos-1 (0. 493)
cos 30˚ =
cos 69˚ =
cos 47˚ =
cos 23˚ =
cos 54˚ =
cos 62˚ =
cos 73˚ =
cos 78˚ =
cos 90˚ =
cos 4˚ =
x˚=
cos x˚ = 0.639
x ˚ = cos -1 (
x˚=
cos x˚ = 0.866
x˚=
x˚=
)
cos x˚ = 0.234
x˚=
x˚=
cos x˚ = 0.248
x ˚ = cos -1 (
x˚=
cos x˚ = 0.618
x˚=
x˚=
cos x˚ = 0.478
x˚=
x˚=
cos x˚ = 0.476
x˚=
x˚=
M May
Slide 6
Use your calculator : cos x˚ = 0.493
x ˚ = cos-1 (0. 493)
cos 30˚ = 0.866
cos 69˚ = 0.358
cos 47˚ = 0.682
cos 23˚ = 0.921
cos 54˚ = 0.588
cos 62˚ = 0.469
cos 73˚ = 0.292
cos 78˚ = 0.208
cos 90˚ = 0
cos 4˚ = 0.998
x ˚ = 60.5˚
cos x˚ = 0.866
x ˚ = cos-1(0.866)
x ˚ = 30˚
cos x˚ = 0.639
x ˚ = cos -1 ( 0.639 )
x ˚ = 50.3˚
cos x˚ = 0.234
x ˚ = cos-1(0.234)
x ˚ = 76.5˚
cos x˚ = 0.248
x ˚ = cos -1 ( 0.248)
x ˚ = 75.6˚
cos x˚ = 0.618
x ˚ = cos-1(0.618)
x ˚ = 51.8˚
cos x˚ = 0.478
x ˚ = cos-1(0.478)
x ˚ = 61.4˚
cos x˚ = 0.476
x ˚ = cos-1(0.476)
x ˚ = 61.6˚
M May
Slide 7
Soh Cah Toa
Remember
The cosine of an angle is found using
hypotenuse
Cah
cos x =
x
Adjacent
9
cos x =
15
x
12
12
15
x = cos-1(12/15)
x = 36.9˚
M May